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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 42, Fasc. 1,
pages 163 - 175
DOI: 10.37190/0208-4147.00036
Published online 8.8.2022
 

Ehrhard-type inequality for the isotropic Cauchy distribution on the plane

T. Byczkowski
J. Małecki
T. Żak

Abstract: We prove an analogue of Ehrhard's inequality for the two-dimensional isotropic Cauchy measure. In contrast to the Gaussian case, the inequality is not valid for non-convex sets. We provide the proof for rectangles which are symmetric with respect to one coordinate axis.

2010 AMS Mathematics Subject Classification: Primary 60E05; Secondary 60E07.

Keywords and phrases: Cauchy distribution, Ehrhard-type inequality.

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